Frequency Response of FIR Filters

Graphical Representation of the Frequency ResponseGraphical Representation of the FrequencyResponse• A useful MATLAB function for plotting the frequencyresponse of any discrete-time (digital) filter is freqz()• The interface to freqz() is similar to filter() in that aand b vectors are again required– Recall that the b vector holds the FIR coefficientsand for FIR filters we set a = 1.>> help freqzFREQZ Digital filter frequency response.[H,W] = FREQZ(B,A,N) returns the N-point complex frequency responsevector H and the N-point frequency vector W in radians/sample ofthe filter:jw -jw -jmwjw B(e) b(1) + b(2)e + .... + b(m+1)eH(e) = ---- = ------------------------------------jw -jw -jnwA(e) a(1) + a(2)e + .... + a(n+1)egiven numerator and denominator coefficients in vectors B and A. Thefrequency response is evaluated at N points equally spaced around theupper half of the unit circle. If N isn't specified, it defaults to512.[H,W] = FREQZ(B,A,N,'whole') uses N points around the whole unit circle.H = FREQZ(B,A,W) returns the frequency response at frequenciesdesignated in vector W, in radians/sample (normally between 0 and pi).[H,F] = FREQZ(B,A,N,Fs) and [H,F] = FREQZ(B,A,N,'whole',Fs) returnfrequency vector F (in Hz), where Fs is the sampling frequency (in Hz).H = FREQZ(B,A,F,Fs) returns the complex frequency response at thefrequencies designated in vector F (in Hz), where Fs is the samplingfrequency (in Hz).FREQZ(B,A,...) with no output arguments plots the magnitude andunwrapped phase of the filter in the current figure window.See also filter, fft, invfreqz, fvtool, and freqs.b kECE 2610 Signals and Systems 6–18